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Robot and Servo Drive Lab.
Sensorless IPMSM Drive System Using Saliency
Back-EMF-Based Intelligent Torque Observer
With MTPA Control
IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 10, NO. 2, MAY 2014
Faa-Jeng Lin, Senior Member, IEEE, Ying-Chih Hung, Student Member, IEEE, Jia-Ming Chen, and
Chao-Ming Yeh
Advisor: Prof. Ming-Syhan Wang
Student: Ika Noer Syamsiana
2016/7/14
Department of Electrical Engineering
Southern Taiwan University of Science and
Technology
Outline :





Introduction
Saliency Back-emf-based Rotor Fluxangle
And Speed Estimator With MTPA Control
WFNN Torque Observer
Design And Experimentation
Conclusion
2016/7/14
2
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Robot and Servo Drive Lab.
INTRODUCTION


The permanent magnet synchronous motors (PMSMs) can
basically be divided into three categories:
 1) surface mounted;
 2) inset; and
 3) interior
Moreover, due to the interior PMSM (IPMSM) has many
attractive characteristics such as high-power density, hightorque-to-inertia ratio, wide speed operation range, and free
from maintenance.
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INTRODUCTION

IPMSM
inverter-fed compressor drive system
However, the compressor is usually operated in
a high-temperature environment with corrosive
refrigerant.

The hall sensors and encoder cannot be installed in
the compressor
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ARCHITECTURE OF SENSORLESS MTPA FIELDORIENTED CONTROL SYSTEM FOR IPMSM
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Estimation of Rotor Flux Angle and Speed



The mechanical model-based PLL can be divided into two parts:
1) the torque observer; and
2) the mechanical model of the IPMSM.
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Estimation of Rotor Flux Angle and Speed
IPMSM in synchronous rotating reference frame
v d  rs  pLd
v     L
 q   re d
  re Lq  id   0 




rs  pLq  iq   re  pm 
Can be expressed in the stationary reference frame
 re Lq  Ld  i 
v   rs  pLd
 sin  re 
 i    re  pm  Lq  Ld  reid  piq 
v     L  L 

r

pL
cos

re
d
q
s
d
re 

  
  
 E 
 sin  re 
 E    re  pm  Lq  Ld  re id  piq 

cos

re 

 
 E 
 sin  re 
E   E 

cos

re 

 
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Estimation of Rotor Flux Angle and Speed
E   re  pm  Lq  Ld  reid  piq 
can be estimated using a state filter based on
current observers in stationary reference frame
The saliency back-EMF state filter consists of two parts:
1. the IPMSM model without saliency back-EMF term and
2. two PI current compensators
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Estimation of Rotor Flux Angle and Speed

The estimated saliency back-EMF will approximate the actual
saliency back-EMF of the IPMSM
 Eˆ  t 
 sin  re t 
lim 
 E


ˆ
t  E
  t 
 cos re t  
 Eˆ # 

sin

 E 

re 
ˆ
 ˆ #   sign( re )    E 

E
 E  
 cos  re 
 

 

 

#
#
ˆ
ˆ
ˆ
  E  cos  re  E  cos ˆre  Eˆ sin  re  ˆre
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
Estimation of Rotor Flux Angle and Speed

The rotor speed and angle estimation transfer function is given
as follows :
ˆ rm ˆrm


 rm  rm
Ld  Lq 3
J
s  Kd s 2  K p s  Ki
Ld  Lq
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Js3  Kd s 2  K p s  Ki
Saliency Back-EMF-Based MTPA Control
(a) IPMSM MTPA control trajectory
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Saliency Back-EMF-Based MTPA Control
(b) Saliency back-EMF-based MTPA control.
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Saliency Back-EMF-Based MTPA Control


The torque equation in the d  q axis synchronously rotating
reference frame of the IPMSM is given as follows :


Tem
3P

 pm iq  Ld  Lq id iq , excitation torque
4
Tem
3P
3P
Ld  Lq id iq , reluctance torque

 pm iq 
4
4
The stator phase current can be obtained as follows :
I s  id2  iq2
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Saliency Back-EMF-Based MTPA Control

Assuming the absolute value of the stator current is keeping
constant below its maximum value in the constant torque
region of the IPMSM
2
q
i
dTem
  pm  Ld  Lq id  Ld  Lq   0
diq
id
id 
 pm  
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2
pm
 4Ld  L
2Lq  Ld 
i
2 2
q
q
Saliency Back-EMF-Based MTPA Control

The estimated rotor flux angle equals to the real rotor flux
angle, the saliency back-EMF use MTPA control using
saliency back-EMF state filter

 
  
Eˆ  Eˆ   sin ˆre  Eˆ  cos ˆre
2
2
ˆ
E  E sin  re  E cos re  E
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Saliency Back-EMF-Based MTPA Control
i 
2
d
L
 pm
d
 Lq 
id  i  0
2
q
2
 Eˆ   re  pm


 piq 

Lq  Ld   Ld  Lq
2
id 

i


q

 pm 
 re





Where
Eˆ  re pm
Ld  Lq
 piq
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The proposed
new MTPA
control
is the saliency back-EMF correction term
WFNN TORQUE OBSERVER
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(a) structure of WFNN
(b) triangular functions in membership layer of WFNN;
(c) triangular functions in wavelet layer of WFNN
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Description of WFNN

The j th fuzzy rule of the proposed WFNN can be presented
as follows
1
1
j
1
1
2
R j : if x is M and x is M
j
2
then  j is  w ikik xi1  , i  1,2
Where
i
R j  jth rule of WFNN
 j  internal variable
xi1  input of WFNN
M 1j , M 2j  input of WFNN
ik  ith in kth term wavelet output to node of wavelet sum layer
wik  Wavelet we ights for units in wavelet mechanism layer
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The signal propagation and the basic function in each
layer of the WFNN are :
Layer 1: Input Layer


For every node in this layer


y  f x N   x N  , i  1,2
1
i
Where
1
1
i
1
i
y  output of membership layer 1
1
i


x  e  Eˆ sin  re  ˆre  
1
1
x  e  
1
2
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(the angle estimation error
term of the rotor flux angle)
(the derivative of the angle estimation error term)

Layer 2: Membership Layer
y 2j N   net 2j N 
j  1,2  6


1
1
0
if
y

m


,
y
i
j
j
i  mj  j

 y i1  m j   j

if m j   j y i1 , y i1  m j
j

 y i1  m j   j
if m j y i1  m j   j

j

Where
y  output of membership layer 2
2
j
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
Layer 3: Rule Layer and Wavelet Mechanism
y k3 N   net k3 N    w 3jk y 2j N  , k  1, ,9
j
Where
  the node in the layer
j
w  connecting weight between
3
jk
membership layer and rule layer
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
0

1

x
 m j  4 j
1
i

 j
4 j

1
 1 xi  m j  2 j

2 j
ik xi1    j

 xi1  m j  2 j
1

 j
2 j

1
 1 xi  m j  4 j
 
4 j
j

if xi1  m j  4 j , xi1  m j  4 j
 
Where
if m j  4 j  xi1  m j  2 j
if m j  2 j  xi1  m j
if m j  xi1  m j  2 j
if m j  2 j  xi1  m j  4 j
 k   wikik x 
 k  kth term wavelet mechanism output to node of wavelet layer
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
Layer 4: Consequent Layer
y N   net N    k w y N  , l  1, ,9
4
l

4
l
4
k
3
k
Layer 5: Output Layer
y N   net N    w y N  , o  1
5
o
5
o
5
l
i
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4
l
Online Learning Algorithm for WFNN

The online parameter learning is based on the supervised
learning algorithms to adjust the link weights in layer 5, the
link weights in layer 3, and the parameters of membership
functions in layer 2 using the back-propagation (BP) algorithm
to minimize the following energy function:
1 2
V  e
2
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Layer 5

The error term
V
  5
yo
5
o

Update rule
5

V

y

V
wl5   w1 5   w1 5 o5   w1 o5 yl4
wl
yo wl
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Layer 4

The error term
Vy
V
5 5
  4  5
  o wl
yl
yo y
4
l
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5
o
4
l
Layer 3

The error term
5
4

V

y

y

V
 k3   3   5 o4 l 3   l4 wk4 k
y k
y o yl y k

Update rule
wik   w 2
V
  w2
wik
Vy o5 yl4
y o5 yl4 wik
 w2 l4 y k3 wk41k , i  1

4 3 4
 w2 l y k wk 2 k , i  2
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Layer 2

The error term
Vy y y
V
3 3
  2  5
   k yk
y j
y o y y y
k
5
o
4
l
2
j

Update rule of m j
4
l
3
k
3
k
2
j
Vyo5 yl4yk3y 2j
V
m j  m
 m 5 4 3 2
m j
yo yl yk y j m j


1
1
0
if
y

m


,
y
i
j
j
i  mj  j


2 1
  m j
if m j   j  y i1  m j
j


2 1
1


if
m

y
j
i  mj  j
 m j 
j

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
Update rule of  j
Vy o5 y l4 y k3 y 2j
V
 j  
   5 4 3 2
 j
y o y l y k y j  j


0

1


y
i  mj
2
   j
2

j

1

y
i  mj
2
   j
 2j

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if y i1  m j   j , y i1  m j   j
if m j   j  y i1  m j
if m j  y i1  m j   j

Where
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
The weights, mean, and standard deviation of the membership
functions are updated as follows:
w N  1  w N   w
5
l
5
l
5
l
wik N 1  wik N   wik
m j N  1  m j N   m j
 j N  1   j N   m j
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DESIGN AND EXPERIMENTATION
Photos of experimental drive system and plant.
(a) IPMSM drive system.
(b) Motor test platform
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The IPMSM manufactured by Rechi Precision
Co., Ltd., Taiwan


The IPMSM is a three-phase Y-connected 4-pole
945 W 220V/6.87A 4000 rpm 22 kg-cm type.
The parameters of the motor at the nominal condition are
given as follows:
r s  0.34  , L d  4.43 mH


L q  9.26 mH , J  0.0005 Nxm/ rad/s 2 ,
B  0.009 Nxmrad/s  ,  pm  0.11.3 Wb
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
The gains of the PI speed controller, the gains of the PI current
controller, and the gains of PID torque observer are given as
follows:
K wp  0.0348 , K wi  0.5512 , K rp  2.3166,
K ri  398.288 , K p  0.0464 , K i  0.3662,
K d  0.0006
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
The rotor flux angle estimation error and the speed error of
speed command tracking are defined as
 re _ error N   ˆre N    re ( N )
rm _ error N   
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*
rm
N   rm ( N )
Simulated Results of Saliency Back-EMF-Based
MTPA Control
(a) Speed responses and speed estimation error of saliency back-EMF-based rotor flux
angle and speed estimator. (b) Current responses of sensorless control without MTPA.
(c) Current responses of conventional MTPA sensorless control. (d) Current responses of
proposed saliency back-EMF-based MTPA sensorless control.
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Experimental Results of Saliency BackEMF-Based MTPA Control
(a) Speed and current responses from 3500 to 4000 rpm without MTPA control at Case 1.
(b) Speed and current responses from 3500 to 4000 rpm without MTPA control at Case 2.
(c) Speed and current responses from 3500 to 4000 rpm with MTPA control at Case 1.
(d) Speed and current responses from 3500 to 4000 rpm with MTPA control at Case 2.
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Experimental results of saliency back-EMFbased MTPA sensorless control
(a) Speed and current responses from 0 to 4000 rpm with PID torque observer at Case 1.
(b) Speed and current responses from 0 to 4000 rpm with PID torque observer at Case 2.
(c) Speed error, input, and output of PID torque observer at Case 1.
(d) Speed error, input, and output of PID torque observer at Case 2.
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Experimental results of saliency back-EMF-based
MTPA sensorless control
(e) Speed and current responses from 0 to 4000 rpm with FNN torque observer at Case 1.
(f) Speed and current responses from 0 to 4000 rpm with FNN torque observer at Case 2.
(g) Speed error, input, and output of FNN torque observer at Case 1.
(h) Speed error, input, and output of FNN torque observer at Case 2.
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Experimental results of saliency back-EMF-based MTPA
sensorless control using WFNN torque observer
(a) Speed and current responses from 0 to 4000 rpm at Case 1.
(b) Speed and current responses from 0 to 4000 rpm at Case 2.
(c) Speed error, input, and output of WFNN torque observer at Case 1.
(d) Speed error, input, and output of WFNN torque observer at Case 2.
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Comparison of PID, FNN and WFNN torque observers of saliency
back-EMF-based MTPA sensorless control at Case 2
(a)–speed and rotor flux angle estimation
error using PID torque observer from 3000
to 3500 rpm,
(b)–speed and rotor flux angle estimation
error using FNN torque observer from 3000
to 3500 rpm,
(c)–speed and rotor flux angle estimation
error using WFNN torque observer from
3000 to 3500 rpm
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Comparison of PID, FNN and WFNN torque observers of
saliency back-EMF-based MTPA sensorless control at Case 2
(d)–performance measurings of rotor flux angle estimation error, and
(e)–performance measurings of speed estimation error
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CONCLUSION


The WFNN torque observer has been proposed to replace the
traditional PID observer used in the conventional saliency
back-EMF-based rotor flux angle and speed estimator to
improve the estimating performance of the rotor flux angle and
speed
The simulated and experimental results have verified the
proposed saliency back-EMF-based rotor flux angle and speed
estimator using WFNN torque observer combine with a new
MTPA control resulted in better estimating and control
performance than the conventional saliency back-EMF-based
rotor flux angle and speed estimator.
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REFERENCES
C. T. Pan and S. M. Sue, “A linear maximum torque per
ampere control for IPMSM drives over full-speed range”,
IEEE Trans. Energy Convers., vol. 20, no. 2, pp. 359366, Jun., 2005, IEEE.
2. A. Consoli, S. Musumeci, A. Raciti and A. Testa, “Sensorless
vector and speed control of brushless motor drives”, IEEE
Trans. Ind. Electron., vol. 41, no. 1, pp. 91-96, Feb., 1994,
IEEE.
3. C. French and P. Acarnley, “Control of permanent magnet
motor drives using a new position estimation technique”,
IEEE Trans. Ind. Appl., vol. 32, no. 5, pp. 10891097, Sep./Oct., 1996, IEEE
1.
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